Preseason Rankings Affecting March Madness Results

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#Hypothesis-Preseason rankings affect march madness results

library(readxl)
library(readr)

getwd()

## [1] "/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file"

setwd("/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file")

CFB_Data <- read.csv("CBB Preseason Rankings.csv")

length(CFB_Data)

## [1] 4

head(CFB_Data)

dim(CFB_Data)

## [1] 250   4

summary(CFB_Data)

##       Year           Rank        Team               Round      
##  Min.   :2009   Min.   : 1   Length:250         Min.   :0.000  
##  1st Qu.:2011   1st Qu.: 7   Class :character   1st Qu.:1.000  
##  Median :2014   Median :13   Mode  :character   Median :2.000  
##  Mean   :2014   Mean   :13                      Mean   :2.436  
##  3rd Qu.:2016   3rd Qu.:19                      3rd Qu.:3.000  
##  Max.   :2018   Max.   :25                      Max.   :7.000

str(CFB_Data)

## 'data.frame':    250 obs. of  4 variables:
##  $ Year : int  2018 2018 2018 2018 2018 2018 2018 2018 2018 2018 ...
##  $ Rank : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Team : chr  "DUKEDuke" "UVAVirginia" "UNCNorth Carolina" "GONZGonzaga" ...
##  $ Round: int  4 7 3 4 5 3 4 3 6 3 ...

colSums(is.na(CFB_Data))

##  Year  Rank  Team Round 
##     0     0     0     0

names(CFB_Data)

## [1] "Year"  "Rank"  "Team"  "Round"

CFB_Data

# Filter for Rank 1
rank1_data <- subset(CFB_Data, Rank == 1)

# Count the number of times each team has been ranked #1
rank1_counts <- table(rank1_data$Team)

rank1_counts

## 
##          DUKEDuke        INDIndiana          KUKansas        UKKentucky 
##                 3                 1                 1                 2 
## UNCNorth Carolina     VILLVillanova 
##                 2                 1

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.2

# Filter for top 5 ranks
top5_data <- subset(CFB_Data, Rank <= 5)

# Count the number of times each team has been in the top 5
top5_counts <- as.data.frame(table(top5_data$Team))

# Rename columns for clarity
names(top5_counts) <- c("Team", "Count")

# Create the bar plot
ggplot(top5_counts, aes(x = reorder(Team, Count), y = Count)) +
  geom_bar(stat = "identity", fill = "orange") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  labs(x = "Team", y = "Number of Times in Top 5", title = "Number of Times Teams Ranked in Top 5")

library(gridExtra)
# Filter for top 5 ranks
top5_data <- subset(CFB_Data, Rank <= 5)

# Prepare the data for plotting
# Create a table counting the number of top 5 ranks for each team by year
top5_yearly_counts <- as.data.frame(table(Year = top5_data$Year, Team = top5_data$Team))

# Rename columns for clarity
names(top5_yearly_counts) <- c("Year", "Team", "Count")

# Generate a list of unique teams
teams <- unique(top5_yearly_counts$Team)

# Plot the data in separate graphs (could use a loop or lapply for this)
plots <- lapply(teams, function(team) {
  team_data <- subset(top5_yearly_counts, Team == team)
  ggplot(team_data, aes(x = Year, y = Count)) +
    geom_line() +
    geom_point() +
    scale_y_continuous(limits = c(0, max(top5_yearly_counts$Count)), breaks = 0:max(top5_yearly_counts$Count)) +
    labs(title = paste("Top 5 Rankings Over Years:", team))
})

# Determine the number of columns and rows based on the number of plots
num_of_plots <- length(plots)
num_of_cols <- ceiling(sqrt(num_of_plots))
num_of_rows <- ceiling(num_of_plots / num_of_cols)

# Arrange the plots into a grid
do.call(grid.arrange, c(plots, ncol = num_of_cols, nrow = num_of_rows))

## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
## ℹ Do you need to adjust the group aesthetic?
## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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## `geom_line()`: Each group consists of only one observation.
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# Assuming your data frame is named CFB_Data and it has 'Rank' and 'Round' columns
# Calculate the Pearson correlation coefficient
correlation <- cor(CFB_Data$Rank, CFB_Data$Round, method = "pearson")

# If the data is not normally distributed or the relationship is not linear,
# use Spearman's rank correlation
correlation_spearman <- cor(CFB_Data$Rank, CFB_Data$Round, method = "spearman")

# Output the correlation coefficient
correlation

## [1] -0.4589596

correlation_spearman

## [1] -0.4608207

library(ggplot2)

ggplot(CFB_Data, aes(x = Rank, y = Round)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  labs(x = "Preseason Ranking", y = "Tournament Round Reached", 
       title = "Correlation between Preseason Rankings and Tournament Performance")

## `geom_smooth()` using formula = 'y ~ x'

library(ggplot2)
# Define what we mean by 'lower-ranked' and 'successful run'
lower_rank_threshold <- 15
successful_run_threshold <- 4

# Create the plot
ggplot(CFB_Data, aes(x = Rank, y = Round)) +
  geom_point(aes(color = (Rank > lower_rank_threshold & Round > successful_run_threshold))) +
  scale_color_manual(values = c('FALSE' = 'black', 'TRUE' = 'red')) +
  geom_smooth(method = "lm", se = FALSE, color = 'blue') +
  labs(x = "Preseason Ranking", y = "Tournament Round Reached", 
       title = "Highlighting Lower-Ranked Teams with Successful Tournament Runs") +
  theme_minimal() +
  theme(legend.position = "none")

## `geom_smooth()` using formula = 'y ~ x'

# Define what we mean by 'lower-ranked' and 'successful run'
lower_rank_threshold <- 15
successful_run_threshold <- 4

# Identify the underdog moments
underdogs <- subset(CFB_Data, Rank > lower_rank_threshold & Round > successful_run_threshold)

# Create the plot
p <- ggplot(CFB_Data, aes(x = Rank, y = Round)) +
  geom_point(aes(color = (Rank > lower_rank_threshold & Round > successful_run_threshold))) +
  scale_color_manual(values = c('FALSE' = 'black', 'TRUE' = 'red')) +
  geom_smooth(method = "lm", se = FALSE, color = 'blue') +
  labs(x = "Preseason Ranking", y = "Tournament Round Reached", 
       title = "Highlighting Lower-Ranked Teams with Successful Tournament Runs") +
  theme_minimal() +
  theme(legend.position = "none")

# Annotate underdog teams
p <- p + geom_text(data = underdogs, aes(label = paste(Team, Year, sep=", ")), 
                   vjust = -1, hjust = 1, color = 'red')

# Print the plot
print(p)

## `geom_smooth()` using formula = 'y ~ x'

# Load necessary libraries
library(ggplot2)
library(readr)

# Read the annual performance data
annual_performance <- read_csv("/Users/shaunmckellarjr/Desktop/College Basketball Project/annual_performance.csv")

## Rows: 10 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): Year, Round
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Plot the time series of the average tournament round reached
ggplot(annual_performance, aes(x = Year, y = Round)) +
  geom_line() +  # Add a line to connect the points
  geom_point() +  # Add points to represent each year
  theme_minimal() +  # Use a minimal theme for the plot
  labs(title = "Average Tournament Round Reached by Top 5 Preseason Ranked Teams",
       x = "Year",
       y = "Average Tournament Round Reached")

# Load the necessary libraries
library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:gridExtra':
## 
##     combine

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(readr)

# Load your dataset
CFB_Data <- read_csv("/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file/CBB Preseason Rankings.csv")

## Rows: 250 Columns: 4

## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Team
## dbl (3): Year, Rank, Round
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Filter for "DUKEDuke" data
duke_data <- CFB_Data %>%
  filter(Team == "DUKEDuke") %>%
  group_by(Year) %>%
  summarize(AverageRound = mean(Round))

# Plot the yearly performance trend for "DUKEDuke"
ggplot(duke_data, aes(x = Year, y = AverageRound)) +
  geom_line() +
  geom_point() +
  theme_minimal() +
  labs(title = "Yearly Tournament Performance Trend for Duke",
       x = "Year", 
       y = "Average Tournament Round Reached")

# Load the necessary libraries
library(ggplot2)
library(dplyr)
library(readr)

# Load your dataset
CFB_Data <- read_csv("/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file/CBB Preseason Rankings.csv")

## Rows: 250 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Team
## dbl (3): Year, Rank, Round
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Now, let's calculate the average tournament round reached for each rank for each year.
rank_performance_over_time <- CFB_Data %>%
  group_by(Year, Rank) %>%
  summarize(AverageRound = mean(Round), .groups = 'drop')

# Plot the general trend of ranks over the years.
ggplot(rank_performance_over_time, aes(x = Rank, y = AverageRound, group = Year)) +
  geom_line(aes(color = factor(Year))) +
  geom_point(aes(color = factor(Year))) +
  theme_minimal() +
  labs(title = "Tournament Outcome Trends Based on Preseason Ranks Over Years",
       x = "Preseason Rank", 
       y = "Average Tournament Round Reached",
       color = "Year")

library(ggplot2)
library(dplyr)
library(readr)

# Load your dataset
CFB_Data <- read_csv("/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file/CBB Preseason Rankings.csv")

## Rows: 250 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Team
## dbl (3): Year, Rank, Round
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# For simplicity, let's start by looking at the trend for rank 1 only.
rank1_data <- CFB_Data %>%
  filter(Rank == 1) %>%
  group_by(Year) %>%
  summarize(AverageRound = mean(Round), .groups = 'drop')

# Plot the trend for rank 1
ggplot(rank1_data, aes(x = Year, y = AverageRound)) +
  geom_line() +
  geom_point() +
  theme_minimal() +
  labs(title = "Yearly Tournament Performance Trend for Rank 1 Teams",
       x = "Year", 
       y = "Average Tournament Round Reached")

# Calculate statistical summaries for each rank
rank_summaries <- CFB_Data %>%
  group_by(Rank) %>%
  summarize(MedianRound = median(Round),
            IQR = IQR(Round),
            .groups = 'drop')

# View the statistical summaries
print(rank_summaries)

## # A tibble: 25 × 3
##     Rank MedianRound   IQR
##    <dbl>       <dbl> <dbl>
##  1     1         4    1.75
##  2     2         4.5  4.25
##  3     3         3    2.5 
##  4     4         4    1.75
##  5     5         3    2.5 
##  6     6         3    3   
##  7     7         3    1.75
##  8     8         3    1.75
##  9     9         4.5  2.75
## 10    10         2.5  2.75
## # ℹ 15 more rows

# Load the necessary libraries
library(ggplot2)
library(dplyr)
library(readr)

# Load your dataset
CFB_Data <- read_csv("/Users/shaunmckellarjr/Desktop/College Basketball Project/Excel file/CBB Preseason Rankings.csv")

## Rows: 250 Columns: 4
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Team
## dbl (3): Year, Rank, Round
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Make sure 'Year' is treated as numeric, which is necessary for regression
CFB_Data$Year <- as.numeric(CFB_Data$Year)

# Calculate the average round reached for each rank in each year
rank_performance <- CFB_Data %>%
  group_by(Year, Rank) %>%
  summarize(AverageRound = mean(Round), .groups = 'drop')

# Now we'll create a list of linear models, one for each rank
model_list <- list()
for(rank in unique(CFB_Data$Rank)) {
  model_data <- rank_performance %>% filter(Rank == rank)
  model_list[[as.character(rank)]] <- lm(AverageRound ~ Year, data = model_data)
}

# Summarize the models
model_summaries <- lapply(model_list, summary)

# Print the summaries for each rank
model_summaries

## $`1`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2485 -0.6500 -0.4000  0.8849  2.1697 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -276.7697   325.9606  -0.849    0.421
## Year           0.1394     0.1619   0.861    0.414
## 
## Residual standard error: 1.47 on 8 degrees of freedom
## Multiple R-squared:  0.08482,    Adjusted R-squared:  -0.02958 
## F-statistic: 0.7414 on 1 and 8 DF,  p-value: 0.4143
## 
## 
## $`2`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3939 -2.0379  0.0758  2.1288  2.5758 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) -56.5151   534.0139  -0.106    0.918
## Year          0.0303     0.2652   0.114    0.912
## 
## Residual standard error: 2.409 on 8 degrees of freedom
## Multiple R-squared:  0.001629,   Adjusted R-squared:  -0.1232 
## F-statistic: 0.01305 on 1 and 8 DF,  p-value: 0.9118
## 
## 
## $`3`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.6364 -1.0864 -0.1273  0.7591  3.1454 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -216.8545   433.6804  -0.500    0.631
## Year           0.1091     0.2154   0.506    0.626
## 
## Residual standard error: 1.956 on 8 degrees of freedom
## Multiple R-squared:  0.03107,    Adjusted R-squared:  -0.09005 
## F-statistic: 0.2565 on 1 and 8 DF,  p-value: 0.6262
## 
## 
## $`4`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3879 -0.9742 -0.1727  0.8061  3.3879 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -448.0121   402.3305  -1.114    0.298
## Year           0.2242     0.1998   1.122    0.294
## 
## Residual standard error: 1.815 on 8 degrees of freedom
## Multiple R-squared:  0.136,  Adjusted R-squared:  0.02802 
## F-statistic: 1.259 on 1 and 8 DF,  p-value: 0.2943
## 
## 
## $`5`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##   -1.8   -1.3   -0.4    0.7    2.8 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -399.0000   390.3066  -1.022    0.337
## Year           0.2000     0.1938   1.032    0.332
## 
## Residual standard error: 1.761 on 8 degrees of freedom
## Multiple R-squared:  0.1174, Adjusted R-squared:  0.007117 
## F-statistic: 1.065 on 1 and 8 DF,  p-value: 0.3324
## 
## 
## $`6`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3091 -0.3773 -0.1364  0.3106  2.2485 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -1119.8788   292.7459  -3.825  0.00505 **
## Year            0.5576     0.1454   3.835  0.00498 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.321 on 8 degrees of freedom
## Multiple R-squared:  0.6477, Adjusted R-squared:  0.6037 
## F-statistic: 14.71 on 1 and 8 DF,  p-value: 0.004982
## 
## 
## $`7`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.5515 -0.7212  0.1091  0.9318  1.8364 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 197.84848  309.79870   0.639    0.541
## Year         -0.09697    0.15386  -0.630    0.546
## 
## Residual standard error: 1.398 on 8 degrees of freedom
## Multiple R-squared:  0.0473, Adjusted R-squared:  -0.07178 
## F-statistic: 0.3972 on 1 and 8 DF,  p-value: 0.5461
## 
## 
## $`8`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7030 -0.7333  0.1030  0.4985  1.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 235.1576   260.0136   0.904    0.392
## Year         -0.1152     0.1291  -0.892    0.399
## 
## Residual standard error: 1.173 on 8 degrees of freedom
## Multiple R-squared:  0.09041,    Adjusted R-squared:  -0.02329 
## F-statistic: 0.7952 on 1 and 8 DF,  p-value: 0.3986
## 
## 
## $`9`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.08485 -1.24091 -0.00909  1.25455  2.76364 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 345.6848   440.7478   0.784    0.455
## Year         -0.1697     0.2189  -0.775    0.460
## 
## Residual standard error: 1.988 on 8 degrees of freedom
## Multiple R-squared:  0.06988,    Adjusted R-squared:  -0.04639 
## F-statistic: 0.601 on 1 and 8 DF,  p-value: 0.4605
## 
## 
## $`10`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2667 -1.1500  0.1333  1.3500  2.2667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept) 539.5333   403.7160   1.336    0.218
## Year         -0.2667     0.2005  -1.330    0.220
## 
## Residual standard error: 1.821 on 8 degrees of freedom
## Multiple R-squared:  0.1811, Adjusted R-squared:  0.0787 
## F-statistic: 1.769 on 1 and 8 DF,  p-value: 0.2202
## 
## 
## $`11`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0000 -1.8833  0.2333  0.7500  4.2000 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 137.13333  534.64091   0.256    0.804
## Year         -0.06667    0.26553  -0.251    0.808
## 
## Residual standard error: 2.412 on 8 degrees of freedom
## Multiple R-squared:  0.007818,   Adjusted R-squared:  -0.1162 
## F-statistic: 0.06304 on 1 and 8 DF,  p-value: 0.8081
## 
## 
## $`12`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.76364 -0.46667 -0.00606  0.50909  2.04242 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -193.04848  257.85696  -0.749    0.475
## Year           0.09697    0.12806   0.757    0.471
## 
## Residual standard error: 1.163 on 8 degrees of freedom
## Multiple R-squared:  0.06688,    Adjusted R-squared:  -0.04976 
## F-statistic: 0.5733 on 1 and 8 DF,  p-value: 0.4706
## 
## 
## $`13`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.6182 -1.3318 -0.6242  1.1621  3.3697 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  27.00606  387.05004   0.070    0.946
## Year         -0.01212    0.19223  -0.063    0.951
## 
## Residual standard error: 1.746 on 8 degrees of freedom
## Multiple R-squared:  0.0004968,  Adjusted R-squared:  -0.1244 
## F-statistic: 0.003976 on 1 and 8 DF,  p-value: 0.9513
## 
## 
## $`14`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0485 -0.9530 -0.4424  1.1954  2.9091 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -83.52121  373.83957  -0.223    0.829
## Year          0.04242    0.18567   0.228    0.825
## 
## Residual standard error: 1.686 on 8 degrees of freedom
## Multiple R-squared:  0.006484,   Adjusted R-squared:  -0.1177 
## F-statistic: 0.05221 on 1 and 8 DF,  p-value: 0.825
## 
## 
## $`15`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9394 -0.6000 -0.1485  0.9803  1.6424 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -193.64848  267.21599  -0.725    0.489
## Year           0.09697    0.13271   0.731    0.486
## 
## Residual standard error: 1.205 on 8 degrees of freedom
## Multiple R-squared:  0.06256,    Adjusted R-squared:  -0.05462 
## F-statistic: 0.5339 on 1 and 8 DF,  p-value: 0.4858
## 
## 
## $`16`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.8606  0.1273  0.2000  0.2545  1.3091 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  50.61212  242.22348   0.209    0.840
## Year         -0.02424    0.12030  -0.202    0.845
## 
## Residual standard error: 1.093 on 8 degrees of freedom
## Multiple R-squared:  0.005051,   Adjusted R-squared:  -0.1193 
## F-statistic: 0.04061 on 1 and 8 DF,  p-value: 0.8453
## 
## 
## $`17`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.39394 -0.73636 -0.05152  0.79394  1.41818 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -376.9939   237.5679  -1.587    0.151
## Year           0.1879     0.1180   1.592    0.150
## 
## Residual standard error: 1.072 on 8 degrees of freedom
## Multiple R-squared:  0.2407, Adjusted R-squared:  0.1458 
## F-statistic: 2.536 on 1 and 8 DF,  p-value: 0.15
## 
## 
## $`18`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9273 -1.7636 -0.8455  1.9909  4.3636 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 149.03636  596.70259   0.250    0.809
## Year         -0.07273    0.29635  -0.245    0.812
## 
## Residual standard error: 2.692 on 8 degrees of freedom
## Multiple R-squared:  0.007472,   Adjusted R-squared:  -0.1166 
## F-statistic: 0.06023 on 1 and 8 DF,  p-value: 0.8123
## 
## 
## $`19`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0242 -0.2667 -0.1000  0.3697  2.2182 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -242.4606   284.6214  -0.852    0.419
## Year           0.1212     0.1414   0.857    0.416
## 
## Residual standard error: 1.284 on 8 degrees of freedom
## Multiple R-squared:  0.08418,    Adjusted R-squared:  -0.0303 
## F-statistic: 0.7353 on 1 and 8 DF,  p-value: 0.4161
## 
## 
## $`20`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9454 -0.4273 -0.2242  0.2273  2.9939 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -376.1939   332.4069  -1.132    0.291
## Year           0.1879     0.1651   1.138    0.288
## 
## Residual standard error: 1.499 on 8 degrees of freedom
## Multiple R-squared:  0.1393, Adjusted R-squared:  0.03175 
## F-statistic: 1.295 on 1 and 8 DF,  p-value: 0.288
## 
## 
## $`21`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1091 -0.9818 -0.5000  0.7500  2.0606 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  49.81212  292.74588   0.170    0.869
## Year         -0.02424    0.14539  -0.167    0.872
## 
## Residual standard error: 1.321 on 8 degrees of freedom
## Multiple R-squared:  0.003463,   Adjusted R-squared:  -0.1211 
## F-statistic: 0.0278 on 1 and 8 DF,  p-value: 0.8717
## 
## 
## $`22`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8182 -0.4394 -0.2121  0.3485  1.3939 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 428.60606  171.49509   2.499   0.0370 *
## Year         -0.21212    0.08517  -2.490   0.0375 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7736 on 8 degrees of freedom
## Multiple R-squared:  0.4367, Adjusted R-squared:  0.3663 
## F-statistic: 6.203 on 1 and 8 DF,  p-value: 0.03749
## 
## 
## $`23`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.21818 -0.40909 -0.10000  0.05909  1.49091 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -474.81818  196.57886  -2.415   0.0422 *
## Year           0.23636    0.09763   2.421   0.0418 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8868 on 8 degrees of freedom
## Multiple R-squared:  0.4229, Adjusted R-squared:  0.3507 
## F-statistic: 5.861 on 1 and 8 DF,  p-value: 0.04178
## 
## 
## $`24`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -1.467 -0.950 -0.200  0.850  1.667 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 135.53333  268.46694   0.505    0.627
## Year         -0.06667    0.13333  -0.500    0.631
## 
## Residual standard error: 1.211 on 8 degrees of freedom
## Multiple R-squared:  0.0303, Adjusted R-squared:  -0.09091 
## F-statistic:  0.25 on 1 and 8 DF,  p-value: 0.6305
## 
## 
## $`25`
## 
## Call:
## lm(formula = AverageRound ~ Year, data = model_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1091 -0.7000 -0.3818  0.8909  1.3455 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -181.34545  213.46607  -0.850    0.420
## Year           0.09091    0.10602   0.857    0.416
## 
## Residual standard error: 0.963 on 8 degrees of freedom
## Multiple R-squared:  0.08418,    Adjusted R-squared:  -0.0303 
## F-statistic: 0.7353 on 1 and 8 DF,  p-value: 0.4161

library(plotly)

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

# Create a ggplot object
p <- ggplot(CFB_Data, aes(x = Rank, y = Round, text = paste(Team, Year, sep=", "))) +
  geom_point(aes(color = (Rank > lower_rank_threshold & Round > successful_run_threshold))) +
  scale_color_manual(values = c('FALSE' = 'black', 'TRUE' = 'red')) +
  geom_smooth(method = "lm", se = FALSE, color = 'blue') +
  labs(x = "Preseason Ranking", y = "Tournament Round Reached", 
       title = "Highlighting Lower-Ranked Teams with Successful Tournament Runs") +
  theme_minimal()

# Convert the ggplot object to a Plotly object
p_plotly <- ggplotly(p, tooltip = "text")

## `geom_smooth()` using formula = 'y ~ x'

# Print the Plotly plot
p_plotly